In this paper, the molecular geometry, vibrational frequencies and chemical shifts of (6-Methoxy-2-oxo-2H-chromen-4-yl)methyl pyrrolidine-1-carbodithioate in the ground state have been calculated using the Hartree-Fock and density functional methods with the 6-311++G(d,p) basis set. To investigate the nonlinear optical properties of the title compound, the polarizability and the first hyperpolarizability were calculated. The conformational properties of the molecule have been determined by analyzing molecular energy properties. Using the time dependent density functional theory, electronic absorption spectra have been calculated. Frontier molecular orbitals, natural bond orbitals, natural atomic charges and thermodynamical parameters were also investigated by using the density functional theory calculations.
Coumarins are wide spread in nature, like flavonoids, which are also extensively represented in plants, and whose beneficial properties have only recently gained recognition . They are structurally closely related to chromenes and show various biological activities [2–6]. Some coumarin derivatives, due to their outstanding optical properties, have also found a place and subsequent use in laser dyes, non-linear optical chromophores, fluorescent whiteners, fluorescent probes and solar energy collectors [7–10]. Because of its unique medicinal properties, structural variability, low cost and low toxicity, the coumarin scaffold has been broadly used in the design and development of a number of pharmaceutically important compounds . Depending on the nature as well as pattern of the substitution, coumarins may display a variety of pharmacological, biochemical and therapeutic properties [12, 13].
By means of increasing development of computational chemistry in the past decade, the research of theoretical modeling of drug design, functional material design, etc., has become much more mature than ever. Many important chemical and physical properties of biological and chemical systems can be predicted from the first principles by various computational techniques . In recent years, density functional theory (DFT) has been a shooting star in theoretical modeling. The development of better and better exchange-correlation functionals made it possible to calculate many molecular properties with comparable accuracies to traditional correlated ab-initio methods, at more favorable computational costs . Literature survey revealed that the DFT has a great accuracy in reproducing the experimental values of geometry, vibrational frequency, electronic absorption spectra, etc. [16, 17].
In the previous publication, the X-ray crystallography and IR spectra of (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate were studied . In spite of its importance, mentioned above, no theoretical calculation concerning (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate has been published yet. The aim of this study is to investigate the spectral and structural properties of the coumarin compound, (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate, using the Hartree-Fock (HF) and density functional theory (DFT) calculations. In this work, the molecular structure, vibrational spectra and assignments, 1H– and 13C NMR spectra, electronic absorption spectra, frontier molecular orbitals (FMO), natural bond orbitals (NBO), natural atomic charges, nonlinear optical properties and thermodynamical parameters of (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate were investigated. These calculations are valuable for providing insight into molecular properties of coumarins.
2 Theoretical methods
The molecular geometry was taken directly from the X-ray diffraction experimental result without any constraints. The HF and DFT calculations of the compound have been done using the Gaussian 09W software . The vibrational frequencies were calculated at the HF and DFT/B3LYP levels for the optimized structures and the predicted frequencies were scaled by 0.96 for DFT/B3LYP and 0.89 for HF. Vibrational band assignments were made using the Gauss-View 5 software . Besides, the thermodynamic functions of the title compound at different temperatures were calculated on the basis of vibrational analysis, using B3LYP/6-311++G(d,p) level. To identify the conformational flexibility, two selected degrees of torsional freedom, T(S1–C18–N6–C19) and T(S1–C17–C14–C15), were changed from –180° to +180° in steps of 10°, and the molecular energy profiles were obtained at the DFT/B3LYP level. The 1H– and 13C–NMR chemical shifts were calculated using the Gauge-Independent Atomic Orbital (GIAO) approach  applying B3LYP and HF methods with 6-311++G(d,p) basis set. The geometry of the compound, together with that of tetramethylsilane (TMS), was fully optimized. The obtained 1H– and 13C–NMR chemical shifts were derived from the equation δ = Σ0 – Σ, where δ is the chemical shift, Σ is the absolute shielding and Σ0 is the absolute shielding of the standard (TMS) . The solvent effect on the theoretical 1H– and 13C–NMR parameters was included using the the integral equation formalism polarisable continuum model (IEF-PCM)  provided by Gaussian 09W. Ethanol and dimethylsulfoxide (DMSO) were used as solvents. The linear polarizability and first hyperpolarizability properties of the title compound were predicted by molecular polarizabilities basing on theoretical calculations. In addition, NBO and FMOs were performed at the B3LYP/6-311++G(d,p) level.
3 Results and discussion
3.1 Optimized geometries
The atomic numbering scheme for the title crystal  and the theoretical geometric structure of the title compound are shown in Fig. 1. The crystal structure of the title compound is triclinic and space group is P-1. The crystal structure parameters are a = 6.7223 (2)Å, b = 8.0369 (2)Å, c = 15.4101 (5)Å, α = 75.320 (2)°, β = 88.482 (1)°, γ = 78.842 (1)° and V = 789.93 (4)Å3 .
The optimized bond lengths, bond angles and torsion angles of the title compound have been obtained using the HF and DFT/B3LYP methods with the 6-311++G(d,p) basis set. Theoretical and experimental geometric parameters are listed in Table 1. When the X-ray structure of the title compound is compared with its optimized counterparts (Fig. 2), slight conformational discrepancies are observed between them. The title crystal is not planar. The dihedral angle between the 2H-chromene (O4/C8–C16) ring and pyrrolidine (N6/C18–C22) ring is 75.24 (16)° for X-ray , whereas the dihedral angle has been calculated as 67.65° for B3LYP and 70.00° for HF. The orientation of the both the rings is defined by the torsion angles C22–N6–C18–S1 (178.00°), N6–C18–S1–C17 (–170.98°), C18–S1–C17–C14 (103.72°) and S1–C17–C14–C15 (–99.35°) which have been calculated as 178.48°, –176.56°, 105.99° and –104.04° for B3LYP, and 178.56°, –174.45°, 98.78° and –107.40° for HF, respectively. In the title compound, the bond lengths and angles are within normal ranges and they are comparable with those of related compounds [24–26].
Selected molecular structure parameters.
|Parameters||Experimental ||Calculated 6-311++G(d,p)|
|Bond lengths [Â]|
|Bond angles [°]|
|Torsion angles [°]|
It is well known that DFT-optimized bond lengths are usually longer and more accurate than HF due to the inclusion of electron correlation . On the other hand, according to calculated results, the HF method correlates better for the bond distance compared with the DFT/B3LYP method (Table 1). The maximum difference of bond lengths between the experimental and the predicted values has been found at C20–C21 bond with the difference being 0.061 Å for B3LYP method, and with a value 0.053 Å for HF method. The root mean square error (RMSE) is obtained as 0.018 Å for HF and 0.021 Å for B3LYP, indicating that the bond lengths predicted by the HF method show a good correlation with the experimental values. For bond angles, the opposite trend was observed. As can be seen from Table 1, both the biggest difference and the RMSE for the bond angles calculated by the B3LYP method are smaller than those predicted by HF. A global comparing of the structures obtained by the theoretical calculations has been done by superimposing the molecular skeleton with that obtained from X-ray diffraction , giving a RMSE of 0.247 Å for B3LYP and 0.324 Å for HF method (Fig. 2). As a result, the B3LYP calculation well reproduces the the 3-D geometry of the title compound.
3.2 Conformational analysis
In order to define the preferential position of pyrrolidine and chrome rings, a preliminary search of low energy structures was performed using B3LYP/6-311++G(d,p) computations as a function of the selected degrees of torsional freedom T(S1–C18–N6–C19) and T(S1–C17–C14–C15). The respective values of the selected degrees of torsional freedom, T(S1–C18–N6–C19) and T(S1–C17–C14–C15), are –0.81° and –99.34° in X-ray structure , whereas the corresponding values in DFT optimized geometry are –1.35° and –104.04°. Molecular energy profiles with respect to rotations about the selected torsion angles are presented in Fig. 3.
As can be seen from the Fig. 3, the low energy domains for T(S1–C18–N6–C19) are located at 0° and 180°, while they are located at –100° and 120° for T(S1–C17–C14–C15). Energy difference between the most favorable and unfavorable conformers, which arises from rotational potential barrier calculated with respect to the two selected torsion angles, is 0.036 Hartree for T(S1–C18–N6–C19) and 0.14 Hartree for T(S1–C17–C14–C15), when both selected degrees of torsional freedom are considered. It must be remarked that the selected torsion angles in the crystal structure of the title compound are close to the value in the global energy minimum.
3.3 Vibrational analysis
In this study, harmonic vibrational frequencies were calculated using the DFT/B3LYP and HF methods with the 6-311++G(d,p) basis set. Using the Gauss-View molecular visualisation program, the vibrational band assignments were made. In order to facilitate assignment of the observed peaks, the vibrational frequencies have been analyzed and the calculation for the title compound have been compared with the experimental results. The vibrational frequencies in the region 4000 cm−1 to 600 cm−1 are given in Table 2. The IR spectra contain some characteristic bands of the stretching vibrations of the C–H, C–H2, C–H3, C=O, C–O, C–N, C=S and C–S groups.
Comparison of the experimental and calculated vibrational frequencies [cm−1].
|Assignmentsa||Experimental ||Scaled frequencies with 6-311++G(d,p)|
3.3.1 C–H vibrations
C–H is known as characteristic vibrational frequency. In the literature, the in-plane and out-of-plane bending vibrational frequencies are obtained within their characteristic region. The aromatic compounds commonly exhibit C–H stretching vibrations in the region of 3150 cm−1 to 2900 cm−1 [29, 30] which is the characteristic region for the ready identification of C–H stretching vibrations in plane. In this region the bands are not appreciably affected by the nature of the substituents. In our present work, C–H aromatic stretching are of medium intensity and in the expected region, lie within the range of 3089 cm−1 to 3078 cm−1 by B3LYP and 3019 cm−1 to 2998 cm−1 by HF. Also C–H in-plane and out-of-plane bending vibrations were observed in the range of 1300 cm−1 to 1000 cm−1 and 900 cm−1 to 675 cm−1 , respectively. In the title compound, C–H aromatic rocking bands have been found at 1348 cm−1, 1184 cm−1 and 1092 cm−1 by B3LYP and at 1344 cm−1, 1205 cm−1 and 1076 cm−1 by HF method. Besides, C–H aromatic wagging bands are only out-of-plane bending vibrations which is observed at 871 cm−1, 816 cm−1 and 728 cm−1 by B3LYP and 887 cm−1, 832 cm−1 and 731 cm−1 by HF. Rahman et al.  has found the wagging type vibrations of the C–H bonds at 820 cm−1 and 794 cm−1 theoretically, which correlates nicely with an experimental peak at 800 cm−1.
3.3.2 Methyl group vibrations
The title molecule possesses one C–H3 group. The C–H methyl group stretching vibrations are highly localized and generally observed in the range of 3000 cm−1 to 2900 cm−1 [31, 33]. In 7-Methoxy-4-methylcoumarin, the bands observed at 3001 cm−1, 2964 cm−1, 2951 cm−1 in FT-IR spectrum and the bands observed at 3000 cm−1 and 2951 cm−1 in Raman spectrum were assigned to CH3 asymmetric stretching vibrations . The CH3 symmetric stretching vibrations were observed at 2902 cm−1 and 2855 cm−1 in the FT-IR spectrum . In this study, the peaks calculated at 3011 cm−1 and 2938 cm−1 for B3LYP and 2924 cm−1 and 2866 cm−1 for HF are assigned to asymmetric stretching of the methyl group.
The symmetric one is calculated at 2883 cm−1 and 2813 cm−1 for B3LYP and HF levels, respectively. CH3 scissoring vibration is also identified at 1460 cm−1 for B3LYP, while wagging vibrations are identified at 1444 cm−1, 1184 cm−1, 1158 cm−1 and 1120 cm−1 and 1450 cm−1, 1205 cm−1, 1181 cm−1 and 1045 cm−1 for B3LYP and HF, respectivly. The calculated wavenumbers of CH3 group vibrations show the good correlation with the data presented in the literature [35–37].
3.3.3 Methylene vibrations
The asymmetric CH2 stretching vibrations are generally observed above 3000 cm−1, while the symmetric stretch appears between 3000 cm−1 and 2900 cm−1 . The CH2 asymmetric stretching vibration was calculated at 2985 cm−1 for B3LYP and at 2889 cm−1 for HF, while the symmetric stretching vibrations were predicted at 2926 cm−1 and 2924 cm−1 for B3LYP and at 2887 cm−1 and 2883 cm−1 for HF. Similar vibrational modes were also observed for free pyrrolidine  or cyclopentene  and other pyrrolidine derivatives . The CH2 two wagging and two twisting out-of-plane deformation vibrations were calculated at 1319 cm−1 and 1184 cm−1 for B3LYP and at 1335 cm−1 and 1205 cm−1 for HF and at 1158 cm−1 and 1128 cm−1 for B3LYP and at 1181 cm−1 for HF, respectively. The band at 910 cm−1 was assigned to CH2 rocking in-plane deformation vibration . In the present work, the same vibrations were calculated at 900 cm−1 by B3LYP and at 935 cm−1 by HF.
3.3.4 C=O and C–O vibrations
Coumarin derivative compounds have two characteristic absorption bands arising from C=O and C–O stretching vibrations. The C=O stretching frequency appears strongly in the IR spectrum in the range of 1600 cm−1 to 1850 cm−1 because of the large change in dipole moment. The carbonyl group vibrations give rise to characteristic bands in vibration spectra and the characteristic frequency used to study a wide range of compounds. The intensity of these bands can increase owing to conjugation or formation of hydrogen bonds . Moghaddam et al.  assigned C=O stretching absorption in the region of 1744 cm−1 to 1717 cm−1 for 3-benzyl-2H-pyrano3,2-chromene-2,5(6H)-dione. In 4-hydroxy-1-thiocoumarin, the C=O stretching was found to be present at 1701 cm−1 . In the present study, chromene (C=O) bond stretching vibration was observed at 1708 cm−1 experimentally , while it has been calculated at 1722 cm−1 for B3LYP and at 1767 cm−1 for HF. The experimental C–O stretching bands were observed at 1036 cm−1 and 1279 cm−1, and were calculated at 900 cm−1 to 1214 cm−1 for B3LYP and at 935 cm−1 to 1233 cm−1 for HF. These values are in good agreement with the similar compounds [45, 46].
3.3.5 C–N vibrations
The calculation of C–N stretching frequency is a rather hard job since there are problems in identifying these frequencies from other vibrations . Silverstein et al.  identified the C–N stretching absorption in the region of 1382 cm−1 to 1266 cm−1 for aromatic amines. Tecklenburg et al.  located the C–N symmetric stretch in the region of 1120 cm−1 to 1150 cm−1. The C–N stretchings were also found to be present at 1248 cm−1 and 1199 cm−1 by Pajazk et al. . In this study, the C–N stretching vibrations were calculated at 1389 cm−1, 1128 cm−1 and 835 cm−1 by B3LYP and at 1389 cm−1, 1181 cm−1 and 843 cm−1 by HF.
3.3.6 C–C vibrations
The aromatic stretching vibrations are very prominent, as they involve double C=C bond in conjugation with the ring. The ring C=C and C–C stretching vibrations are expected within the region of 1620 cm−1 to 1390 cm−1 . The C=C stretching vibrations of the title compound with very strong intensity are predicted at 1594 cm−1, 1581 cm−1, 1536 cm−1 and 1460 cm−1 for B3LYP level and at 1604 cm−1, 1566 cm−1 and 1475 cm−1 for HF level. These olefinic C=C stretching vibrations are also in good agreement with the experimental (at 1590 cm−1, 1558 cm−1, 1544 cm−1 and 1482 cm−1) and theoretical (1588 cm−1, 1583 cm−1, 1541 cm−1 and 1508 cm−1) values . The stretching vibrational bands for C–C bond were calculated at 1348 cm−1 and 1319 cm−1 for B3LYP and at 1344 cm−1 and 1335 cm−1 for HF.
3.3.7 C=S and C–S vibrations
According to Silverstein et al. , the spectra of the compounds in which C=S group is attached to an N atom show absorption bands in the broad region of 1563 cm−1 to 700 cm−1. In nitrogen containing thiocarbonyl compounds, the assignment of the C=S stretching frequency has been controversial [53–55]. Mani et al.  have reported an absorption band in phenylisothiocynate near 988 cm−1. The absorption bands in the region of 1180 cm−1 to 1150 cm−1 have been assigned to the C=S stretching vibrations in thiohydroxamic acids . In this study, the C=S stretching vibration, calculated at 974 cm−1 for B3LYP and at 972 cm−1 for HF. The C–S group is less polar than carbonyl links and has a considerably weaker band. In consequence, the bond is not intense, and it falls at lower frequencies . Tanak et al.  assigned this mode at 680 cm−1 and 497 cm−1 in FT-IR spectrum. The C–S stretching mode was observed at 672 cm−1 for trifluoperazine . In our title molecule the C–S stretching is observed at 660 cm−1 in FT-IR spectrum . This band is found to be 666 cm−1 and 801 cm−1 for HF, and 674 cm−1 and 792 cm−1 for B3LYP.
3.4 Proton and carbon-13 NMR chemical shift analyses
GIAO 1H and 13C chemical shift values were calculated using B3LYP and HF methods with the 6-311++G(d,p) basis set in gas phase and the calculated results are given in Table 3. To investigate the solvent effect on the chemical shift values of the compound, based on B3LYP and HF method and IEF-PCM model, two solvents (ε = 46.7, DMSO; ε = 24.55, ethanol) were selected and the calculated values were also listed in Table 3. Relative chemical shifts were estimated by using the TMS shielding calculated in advance at the same theoretical level as the reference. Calculated 1H isotropic chemical shielding for TMS at the HF(gas), B3LYP(gas), HF(ethanol), B3LYP(ethanol), HF(DMSO) and B3LYP(DMSO) are 32.44 ppm, 31.97 ppm, 32.43 ppm, 31.96 ppm, 32.43 ppm and 31.96 ppm, respectively. Also, calculated 13C isotropic chemical shielding for TMS at the HF (gas), B3LYP (gas), HF (ethanol), B3LYP (ethanol), HF (DMSO) and B3LYP (DMSO) are 196.11 ppm, 184.06 ppm, 196.58 ppm, 184.54 ppm, 196.59 ppm and 184.66 ppm, respectively.
Theoretical and experimental 1H and 13C isotropic chemical shifts (with respect to TMS values in ppm) for the title compound.
We have calculated 1H chemical shift values (with respect to TMS) of 1.89 ppm to 7.37 ppm at the B3LYP (gas) and 1.73 ppm to 7.81 ppm at HF (gas) level. Besides, they were calculated to be 2.00 ppm to 7.48 ppm at the B3LYP (ethanol),1.71 ppm to 7.80 ppm at the HF (ethanol), 2.00 ppm to 7.49 ppm at the B3LYP (DMSO) and 1.71 ppm to 7.80 ppm at the HF (DMSO). In (S)-2-Oxopyrrolidin-1-yl Butanamide , CH2 protons of the pyrrolidine ring are observed in the region of 2.47 ppm to 4.50 ppm. In our study, CH2 protons of the pyrrolidine ring are found in the region of 1.89 ppm to 4.30 ppm at all the B3LYP levels and 1.73 ppm to 3.88 ppm at all the HF levels. In the 3-(1-((methoxycarbonyl)oxy)imino)ethyl)-2H-chromen-2-one, the chemical schift values of chromene ring protons were observed at 7.28 ppm to 8.08 ppm experimentally, and at 7.05 ppm to 7.91 ppm for the HF/6-311++G(d,p) level and 7.26 ppm to 8.41 ppm for the B3LYP/6-311++G(d,p) level . In the present work, the chromene ring protons have been calculated at 6.80 ppm to 7.87 ppm for B3LYP and at 6.73 ppm to 7.81 ppm for HF levels in gas and solution phase.
The 13 C NMR chemical shift values (with respect to TMS) have been calculated to be 28.69 ppm to 205.44 ppm for B3LYP (gas), 24.57 ppm to 226.88 ppm for HF (gas), 29.23 ppm to 206.75 ppm for B3LYP (ethanol), 25.04 ppm to 227.35 ppm for HF (ethanol), 29.35 ppm to 206.97 ppm for B3LYP (DMSO) and 25.05 ppm to 227.36 ppm for HF (DMSO). The chromene ring carbons give peaks at 100 ppm to 200 ppm for all methods. These peaks have been observed at 113 ppm to 177 ppm in 7-Acetoxy-4-(bromomethyl)coumarin . As seen from Table 3, 1H and 13C NMR spectra were a little affected by the change in polarity of the solvent. 1H and 13C chemical shift results of the title compound in gas phase are generally closer to the solvent phase. The calculated 1H and 13C chemical shift values of the title compound are in a good agreement with those of related chromene and pyrrolidine derivatives [64, 65].
3.5 Natural bond orbital analysis
NBO analysis provides an efficient method for studying intra and intermolecular hydrogen bonding and interaction among bonds, and provides a convenient basis for investigating charge transfer or conjugative interaction in molecular systems. The energy of hyperconjugative interactions or the stabilization energy gives the interaction between donor groups and acceptor ones [66, 67]. More intensive interactions between electron donors and electron acceptors depend on larger E(2) value, i.e., the more donating tendency from electron donors to electron acceptors the greater the extent of conjugation of the whole system . For each donor NBO (i) and acceptor NBO (j), the stabilization energy E(2) is estimated by the following equation [69,70]:
where qi is the donor orbital occupancy, εi, εj are diagonal elements (orbital energies) and Fij is the off-diagonal NBO Fock matrix element. In order to investigate the intramolecular interaction, the stabilization energies of the title compound were performed using the second-order perturbation theory. The results of second-order perturbation theory analysis of the Fock Matrix at B3LYP/6-311++G(d,p) level of theory are collected in Table 4. For the table, the stabilization energies larger than 13 kJ/mol have been chosen.
Selected second-order perturbation energies E(2) associated with i → j delocalization in gas phase.
|Donor orbital (i)||Type||ED/e||Acceptor orbital (j)||Type||ED/e||E(2) [kJ/mol]a||E(j)-E(i) [a.u.]b||F(ij) [a.u.]c|
The NBO analysis has revealed that the intramolecular interactions which are formed by the orbital overlap between bonding (C–S), (C–O), (C–N), (C–C) and (C–H) anti-bonding orbital, result in intramolecular charge transfer causing stabilization of the compound. These interactions are observed as an increase in electron density (ED) in (C–S), (C–C) and (C–O) anti-bonding orbitals that weakens the respective bonds. The electron density of the five conjugated single bonds of pyrrolidine ring (~1.98 e) clearly demonstrates strong delocalization. Additionally, the ED of conjugated bond of 2H-chromene ring (~ 1.91 e) clearly shows strong delocalization inside the compound .
In the studied compound, strong intramolecular hyperconjugative interactions of π-electrons with the greater energy contributions from C8–C9 → C10–C11 (73.94 kJ/mol),C12–C13 (69.93 kJ/mol); C10–C11 → C8–C9 (74.48 kJ/mol), C12–C13 (71.68 kJ/mol); C14–C15 (42.21 kJ/mol); C12–C13 → C8–C9 (80.67 kJ/mol), C10–C11 (75.53 kJ/mol); C14–C15 → O5–C16 (91.54 kJ/mol), C10–C11 (43.76 kJ/mol) are observed for the chromene part of the compound. The hyperconjugative interactions of the σ → σ* and σ → π* transitions occur also from various bonds in the compound, such as the hyperconjugative interaction of the σ(C22–H22B) distribute to σ* (C22–H22B); (C15–H15); (C10–C14)(C14–C17) and (C22–H22A) leading to stabilization of 33.27 kJ/mol, 46.94 kJ/mol, 61.61 kJ/mol, 118.16 kJ/mol and 269.02 kJ/mol, respectively. This enhanced bond further conjugate with antibonding orbital of π* (C14–C15), which results in strong delocalization of 52.54 kJ/mol.
There is a very weak intramolecular C–H... S hydrogen bond exposed in the NBO analysis results shown in Table 4 caused by the interactions between the sulfur lone-pair LP(2) S2 and the antibonding orbital σ*(C17–H17B). The lone pair of N6 donates its electrons to the σ-type antibonding orbital for (S2–C18). This interaction gives the strongest stabilization to the system of the title compound by 357.01 kJ/mol. In addition, the π* (C8–C9) NBO conjugates with respective bonds of π* (C10–C11) and π* (C12–C13) resulting in an enormous stabilization of 532.95 kJ/mol and 830.56 kJ/mol, respectively.
3.6 Atomic charge analysis
In order to investigate the electron population of each atom of the title compound, the natural population analysis (NPA) atomic charges of the compound were calculated using the DFT/B3LYP method with the 6-311++G(d,p) basis set. The obtained results are given in Table 5. NPA charge plot has been shown in Fig. 4. The NPA analysis shows that the carbon atoms attached to hydrogen atoms are negative, whereas the carbon atoms (C8, C11, C16) adjacent to the oxygen atoms of the chromene ring are positively charged. The oxygen atoms of chromene fragment and N6 atom of pyrrolidine ring have more negative atomic charges whereas all the hydrogen atoms have positive charges. The maximum positive atomic charge is obtained for C16 atom of carbonyl group when compared with all other atoms. This is due to the attachment of maximum negatively charged O5 atom.
Natural atomic charges (e) of (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate.
3.7 Electronic absorption spectra and frontier molecular orbital analysis
The electronic absorption spectra of the title compound were computed using the TD-DFT method in the gas phase and the DMSO solvent (Fig. 5). The solvent effect was calculated using IEF-PCM method. For TD-DFT calculations, a theoretical absorption band was calculated at 242.43 nm (3.62 eV) with oscillator strength being 0.104. The other absorption peak was calculated at 231.21 nm (5.36 eV) with oscillator strength being 0.114. In addition to the calculations in gas phase, TD-DFT calculations of the title compound in DMSO solvent were performed at 352.01 nm (3.52 eV) with oscillator strength being 0.127 and at 233.41 nm (5.31 eV) with oscillator strength being 0.208. According to the investigations on the frontier molecular orbital (FMO) energy levels of the title compound, we can find that the corresponding electronic transfers happened between the HOMO–1 and LUMO, HOMO–3 and LUMO+1 orbitals, respectively.
The FMO plays an important role in the electric and optical properties, as well as in UV-Vis spectra and chemical reactions [71, 72]. Fig. 6 shows the distributions and energy levels of calculated at the B3LYP/6-311++G(d,p) level for the title molecule. As can be seen from Fig. 6, both for the HOMO and HOMO–1, the electrons are delocalized on the sulfur atoms of the pyrrolidine-1-carbodithioate. For the LUMO and LUMO+1, the electrons are mainly delocalized on the 2-oxo-2H-chromen ring, C14–C17 bond and S1 atom. The value of the energy separation between the HOMO and LUMO is 1.42 eV. Considering the chemical hardness, small HOMO–LUMO gap (ΔEH−L) means a soft molecule and large ΔEH−L means a hard molecule. One can also relate the stability of the molecule to hardness, which means that the molecule with the least ΔEH−L is more reactive and less stable . The η and S can be calculated using the HOMO and LUMO energy values for a molecule as follows: η = (ELUMO−EHOMO)/2 and S = 1/2η , where ELUMO and EHOMO are LUMO and HOMO energies, respectively. The calculated values of η and S for the title compound are 0.71 eV and 0.70 eV−1, respectively.
3.8 Molecular electrostatic potential
Molecular electrostatic potential (MEP) mapping is very useful for understanding the sites for electrophilic attack and nucleophilic reactions as well as hydrogen bonding interactions . Red-electron rich or partially negative charge regions of MEP are related to electrophilic reactivity and the blue-electron deficient or partially positive charge regions of MEP are related to nucleophilic reactivity shown in Fig. 7. The MEP clearly indicates that the electron rich centres were found around the O3, O5 and S2 atoms. The negative V(r) values are −0.023 a.u. for O3 atom, −0.103 a.u. for O5 and −0.035 a.u. for S2 atom. Thus, it could be predicted that an electrophile would preferentially attack the title molecule at O5 atom. On the other hand, a maximum positive region is localized on the methyl nearby with a value of +0.069 a.u. indicating a possible site for nucleophilic attack. So, the MEP surfaces clearly indicate that positive potential sites are around methylene and methyl hydrogen atoms. These sites give information that the compound can have metallic bonding and intermolecular interactions .
3.9 Non-linear optical properties
Nonlinear optics (NLO) is at the forefront of current research because of its importance in providing the key functions of frequency shifting, optical switching, optical modulation, optical logic, and optical memory for emerging technologies in areas such as telecommunications, signal processing, and optical interconnections [75, 76].
The dipole moment (μ), polarizability (α) and first hyperpolarizbility (β) values of the title molecule were computed at the B3LYP/6-311++G(d,p) level using the Gaussian 09W program package. Calculations of the polar properties (α and β) from the Gaussian output have been explained in detail previously , and DFT has been used extensively as an effective method to investigate organic NLO materials [78, 79].
The calculated values of μ, α and β are 9.007 Debye, 38.299 Å3 and 4.868 esu for the title compound. Urea is used as one of the prototypical molecules in the study of NLO properties of molecular systems. Therefore, it has been used frequently as a threshold value for comparative purposes . The values of α and β of the title compound are greater than those of urea (the α and β of urea are 5.042 Å3 and 0.78 × 10−30 esu obtained using the B3LYP/6-311++G(d,p) method) . Theoretically, the β value of the title compound is of 6.24 times magnitude of urea. When we compare it with the similar compounds in the literature, the calculated value of β of the title compound is smaller than those of 9-methoxy-2H-furo3,2-gchromen-2-one (β = 5.2983 × 10−30 esu calculated with B3LYP/6-311++G(d,p) method)  and 6-phenylazo-3-(p-tolyl)-2H-chromen-2-one (β = 34.528 × 10−30 esu calculated with B3LYP/6-311++G(d,p) method) . According to the magnitude of β , the title coumarin compound may be a potential applicant in the development of NLO materials.
3.10 Thermodynamic properties
The standard thermodynamic functions: entropy
The correlations equations between these thermodynamic properties and temperatures T are as follows:
Thermodynamic properties at different temperatures at B3LYP/6-311++G(d,p) level.
In this study, we have calculated the geometric parameters, vibrational frequencies and chemical shifts of (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate using the DFT/B3LYP and HF methods in conjunction with the 6-311++G(d,p) basis set. The comparisons between the calculated results and the X-ray experimental data show that HF method is better than B3LYP method in evaluating bond lengths. However, the B3LYP method seems to be more appropriate than HF method for predicting the bond angles and 3D geometry of the title compound. The vibrational frequencies are exactly assigned to its molecular structure with the aid of the theoretical calculations at B3LYP/6-311++G(d,p) and HF/6-311++G(d,p) levels, in which the experimental and theoretical results support each other. Furthermore, the calculated electronic absorption wavelengths and 1H and 13C NMR chemical shift values of the title compound in gas phase and solvent media can be built into the database for other chromen and pyrrolidine derivatives. It will be helpful for the design and synthesis of new materials. The stabilization energies were obtained from the second-order perturbation theory. The NBO analysis revealed that the π* → π* interactions give the strongest stabilization to the system. The correlations between the statistical thermodynamic properties (enthalpy, entropy, heat capacity) and temperature were also obtained. The calculated first order hyperpolarizability of the title compound was 6.24 times greater than that of urea.
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Maximum differences between the bond lengths and angles computed using theoretical methods and those obtained from X-ray diffraction
Maximum differences between the bond lengths and angles computed using theoretical methods and those obtained from X-ray diffraction
E(2) energy of hyper conjugative interactions
Energy difference between donor and acceptor i and j NBO orbitals
Fij is the Fock matrix element between i and j NBO orbitals